Re: How many different unit fractions are lessorequal than all unit fractions?

On 10/5/24 2:54 PM, WM wrote:

On 05.10.2024 15:02, joes wrote:

Am Sat, 05 Oct 2024 11:32:44 +0200 schrieb WM:

On 05.10.2024 10:08, joes wrote:

Am Fri, 04 Oct 2024 22:09:41 +0200 schrieb WM:

But it is no quantifier shift but simplest logic:
If ℵ₀ unit fractions do not sit at one point (and are not dark) then
they can be subdivided into smaller parts.

Which they can.

Do it. Fail because slightly fewer is not possible.

What do you mean? All the unit fractions have, as you say,
finite distances, which means there are numbers inbetween.

But these numbers and these unit fractions cannot be found. It is impossible to define a unit fraction having less than ℵo smaller unit fractions. It is impossible to define a unit fraction being closer to zero although it is obvious that there are points closer to zero than ℵo*2^ℵo points.
 Regards, WM
 

But strangely, at least to you, in that set of points are more unit fractions, so your set isn't bellow all of them.
Your problem is you like to generate question about points that just don't exist.
You ASSUME that there is a point below which no unit fractions can be defined, but that point is 0, which is below the limit you need.
ANY finite value above 0 will have Aleph_0 unit fractions below it.
Your math and logic just can't handle that fact, because you are too ignorant to use the right systems, or even to know you need to use better math and logic.